先化简,后求值：(x^2y-4y^3)/(x^2+4xy+4y^3)*((4xy)/(x-2y)+x)其中x=根号2-1y=根号2+1

题目

先化简,后求值：(x^2y-4y^3)/(x^2+4xy+4y^3)*((4xy)/(x-2y)+x)其中x=根号2-1y=根号2+1

答案

题是这样的吧(x^2y-4y^3)/(x^2+4xy+4y^2)*((4xy)/(x-2y)+x),感觉是4y²
原式=y(x+2y)(x-2y)/(x+2y)² * (4xy +x²-2xy)/(x-2y)
=y(x+2y)(x-2y)/(x+2y)² * x(x+2y)/(x-2y)
=xy
∵x=√2-1 ,y=√2+1
∴xy=1
∴原式=1